Is it acceptable to work backwards in a show this problem?

In problems that ask you to "show" something (e.g. "show that the formula/equation for ____ is _____") , it it sufficient to simply justify the answer they give (working backwards to literally "show it"), or should one derive the formula, as if the answer were not there?

I know this depends on the problem, for example, an exercise that asks you show that a particular solution to an ODE is correct probably does not want you to solve the ODE. There are also cases in which it is impossible to work backwards. But, what is the general rule to these problems, if any?

In problems that ask you to "show" something (e.g. "show that the formula/equation for ____ is _____") , it it sufficient to simply justify the answer they give (working backwards to literally "show it"), or should one derive the formula, as if the answer were not there?

I know this depends on the problem, for example, an exercise that asks you show that a particular solution to an ODE is correct probably does not want you to solve the ODE. There are also cases in which it is impossible to work backwards. But, what is the general rule to these problems, if any?

I believe most questions like those expect you to proceed in a direct fashion (defining variables and manipulating them) to find the "target equation/answer".

That's probably almost always the case because if you work backwards, there's far more room for errors and you may potentially find yourself with the "wrong start" if you know what I mean.

Take for example something like Hess' law. Imagine trying to work the target equation backwards to find the 'x' many given equations and molar enthalpies. That's definitely harder than using the x many equations to find the target equation.

I find it that it is easy to plug the variables into the equation. For example if you take the basic equation d=st, then rather than thinking in your brain backwards about numbers, plugging in is a lot easier.

Staff: Mentor

In problems that ask you to "show" something (e.g. "show that the formula/equation for ____ is _____") , it it sufficient to simply justify the answer they give (working backwards to literally "show it"), or should one derive the formula, as if the answer were not there?

If the goal of the exercise is as you state here, you should start with the given assumptions and work toward the formula or equation.

I know this depends on the problem, for example, an exercise that asks you show that a particular solution to an ODE is correct probably does not want you to solve the ODE.

This is really a different question. Here you are given a differential equation and a purported solution. All you need to do is show that the solution that is provided satisfies the D.E. You do not need to solve the differential equation, and doing so is much more work than is asked for.

There are also cases in which it is impossible to work backwards. But, what is the general rule to these problems, if any?

If you are asked to show that two equations are equivalent, then it might be possible to work backward from the equation you're supposed to end with, provided that each step you apply is reversible. For example, operations such as adding a certain quantity to both sides of the equation, multiplying both sides by the same nonzero number, and others are reversible steps. Squaring both sides, however, is not a reversible step.

This is sometimes called a "synthetic" proof: you start from the conclusion and work backwards to the hypothesis. As long as it is clear that every step is reversible that's a valid proof because we could go from hypothesis to conclusion by reversing each step.